The half-life of a sample is the amount of time taken for its mass to decrease by half due to radioactive decay.
Half life equations form the basis of much of the theory behind the physical applications of nuclear science. For example, the principle of an atomic clock relies upon making exact measurements of the half life of a radioactive substance — the amount of time taken for the mass of a sample to decay by half — and using this information to keep very accurate time. Half-life problems are simple with the proper information and formulas.
1. Make a list of the vital pieces of information. In a half-life problem there are five pieces of information that complete the equation and usually the problem will give you some of the information and ask you to work out the rest from that. Draw a rough table with two columns and write “initial mass of sample,” “final mass of sample,” “total time of decay,” “number of half-lives” and “half-life length” in the left hand column.
2. Read the problem carefully and fill in the right hand part of the column with each value. If the question talks about a 50 gram sample of carbon-12, write 50 next to the “initial mass” box. If it talks about the sample being left for five years, write five years next to the “total time of decay” box. This produces a table with all the known and unknown information.
3. If you have the relevant information, divide the final mass of the sample by the initial mass. This gives you the fraction of the original material remaining.
4. Substitute all the information you have discovered so far, either given in the question or derived in step 3, into the equation; fraction of original material = 1 / 2 x (number of half-lives). This can be rearranged to find other information. To find number of half-lives, for example, re-arrange the equation to it reads; 2 x (number of half-lives) = 1 / (fraction of original material). You can solve for the half life by dividing the total time of decay by the number of half lives.